Download "Числа - Часть 2. Бесконечность. Лестница Иакова - Документальный фильм"
%3Aformat(webp)%2Fi.ytimg.com%252Fvi_webp%252FeGEUiqXwISs%252Fmaxresdefault.webp&w=1139&q=75)
Similar videos from our catalog
%3Aformat(webp)%2Fi.ytimg.com%252Fvi_webp%252F1uOfTjnxbDs%252Fmaxresdefault.webp&w=1139&q=75)
%3Aformat(webp)%2Fi.ytimg.com%252Fvi%252F9LcYMtj3BNI%252Fmaxresdefault.jpg&w=1139&q=75)
%3Aformat(webp)%2Fi.ytimg.com%252Fvi_webp%252FL8BSqv5gy4w%252Fmaxresdefault.webp&w=1139&q=75)
%3Aformat(webp)%2Fi.ytimg.com%252Fvi_webp%252FNPpBMdtCy1Y%252Fmaxresdefault.webp&w=1139&q=75)
%3Aformat(webp)%2Fi.ytimg.com%252Fvi_webp%252FU4N_KWfwMTk%252Fmaxresdefault.webp&w=1139&q=75)
%3Aformat(webp)%2Fi.ytimg.com%252Fvi%252FVpyFcd7kwMA%252Fmaxresdefault.jpg&w=1139&q=75)
%3Aformat(webp)%2Fi.ytimg.com%252Fvi_webp%252FW-z7EkRne6U%252Fmaxresdefault.webp&w=1139&q=75)
%3Aformat(webp)%2Fi.ytimg.com%252Fvi%252FlAamYTBrF10%252Fmaxresdefault.jpg&w=1139&q=75)
Video tags
Subtitles
Russian
00:00:00
[music]00:00:26
[music]00:00:43
who is galloping who is studying under the mist of00:00:47
the rider belated00:00:49
with him the young son to his father Vesa Stroganov00:00:53
the baby will accept hugging him holds and warms00:00:56
the old man00:01:01
[music]00:01:05
the father drives the horses to find a00:01:08
safer place in this world child why are00:01:17
you so to me timidly clung to him he wants to00:01:22
hide from the real world, my dear00:01:27
forest king, this sphere of infinity is speaking to me,00:01:31
where no one00:01:35
has looked, my dear forest king, my eyes00:01:41
sparkled,00:01:42
no, my baby misheard you, the wind,00:01:48
waking up, swayed the bushes00:01:55
300:01:57
because.00:02:06
today we will visit the world discovered by one00:02:10
person, the object is fear, the rider00:02:18
is chasing the rider, he galloped00:02:23
the yard in his hands, the dead baby was lying00:02:29
[music]00:02:46
scriptwriter, Kim Mi-ran00:02:49
[music]00:02:51
operator, join joe echo,00:02:57
Lee array music,00:03:04
director, Kim Hyung-jun00:03:06
[music]00:03:09
numbers 5 numbers that changed world00:03:14
part 2 infinity00:03:17
staircase and that's why the Vatican there were times00:03:27
when this small city state00:03:29
ruled all of Europe00:03:45
at the end of the 20th century the Vatican released00:03:49
a document that had been hidden for about 400 years00:04:04
it was a long-awaited and very bold00:04:09
decision00:04:22
this document is a record of a00:04:24
trial that took place in00:04:28
1633 it was the greatest controversy in00:04:31
the history of the Catholic Church00:04:40
Galileo Galilei from Florence who00:04:44
swore to tell the truth and only the truth00:04:47
the priests00:04:48
asked the following question road when did you00:04:56
believe that the sun00:04:59
they the earth is the center of the universe and00:05:03
that the earth moves the site of the new era this is mom00:05:08
here your well00:05:12
Galileo answered the priest that00:05:15
never believed that the earth was the center of the universe,00:05:20
but belief in geocentrism00:05:22
would mean denying the cosmology of all00:05:25
times00:05:31
in that era they believed that the earth was the center of the00:05:33
universe00:05:35
[music]00:05:38
and the sun and planets revolved around it,00:05:45
then there were stars00:05:48
there and the universe ended, it was a00:05:53
completely closed universe,00:06:04
how different were the ideas00:06:06
galleries from the beliefs of that century Basilica of00:06:11
Santa Maria Novella Florence Italy00:06:18
all celestial bodies revolve around the earth00:06:22
of their master geocentrism was convenient00:06:27
for interpreting the relationship of man with God00:06:31
a similar cosmology was reflected in00:06:34
works of art00:06:40
God and angels are larger while00:06:44
worthless people00:06:45
are depicted as small also important00:06:50
people were depicted large even if00:06:53
they were in the background00:07:01
this is the most popular painting in this00:07:03
cathedral00:07:07
and for a very long time the Holy Trinity by Masaccio00:07:11
it was painted in a completely different style than00:07:14
was then accepted what people thought when they00:07:17
first saw this work00:07:20
[music]00:07:25
someone made a recess in the wall00:07:30
this it looks like a painting but how he created00:07:34
this empty space, all they00:07:38
had to do was close their eyes and an00:07:41
endless vat appeared before them it00:07:43
[music]00:07:49
Galileo was the one who looked into this00:07:52
abyss00:07:53
[music]00:07:56
and the abyss was00:07:59
endless00:08:01
[music]00:08:05
British Museum London00:08:10
the first artists to discover infinity were00:08:13
them in mathematics,00:08:19
the technique that amazed those who saw the picture00:08:22
is called perspective00:08:24
[music] the00:08:27
17th century painting reflects the perspective of the00:08:39
little grayling from the Netherlands00:08:47
[applause]00:08:50
the desire to paint realistic canvases00:08:52
gave rise to perspective00:08:55
[applause]00:09:00
but how to depict a three-dimensional landscape on a00:09:03
two-dimensional canvas, this requires00:09:08
the eye of an artist00:09:13
[music]00:09:19
first the artist places his canvas in front of00:09:23
the landscape00:09:25
then the artist looks at a certain00:09:28
point landscapes00:09:32
points are marked on the canvas passing through00:09:35
it and reaches the eyes00:09:38
[music]00:09:42
this happens with more distant00:09:45
points if you connect these points you00:09:51
get a line00:09:54
and this line goes in one direction00:09:58
[music]00:10:04
exists . where 2 infinite straight lines00:10:07
connect00:10:09
but in reality this point exists00:10:14
because in reality these lines are00:10:16
absolutely parallel to each other00:10:20
[music]00:10:24
this is .00:10:26
where infinity exists let's00:10:30
get to this point on the way we00:10:39
will meet someone and pass by houses that00:10:43
have disappeared we move on and together where00:10:50
two roads connect we will meet00:10:53
infinity but the faster you00:10:59
run the days the faster it moves away00:11:02
infinity always runs away00:11:05
it and there is a problem of infinity00:11:19
depth00:11:21
we are face to face with another00:11:24
infinity00:11:26
it may lie right under our feet00:11:33
[music]00:11:34
[applause]00:11:39
[music]00:11:41
this game of dots and lines people must00:11:46
alternate their feet at a00:11:47
distance of 42 kilometers 195 meters00:11:52
marathon greece00:11:56
was born here marathon and also mathematics00:12:02
or philosophy this nation fought with00:12:05
words they used swords00:12:08
[music]00:12:17
at the beginning of the marathon it starts to rain because of00:12:22
such unexpected events00:12:24
the marathon is often compared to life you00:12:29
can’t run too fast because even00:12:31
if you feel good there are00:12:34
difficult moments the main goal is not to win00:12:38
but to reach finish, each race00:12:46
consists of an odd number of moments,00:12:51
let's capture these moments,00:12:59
here is one of them, but is it so,00:13:04
what if00:13:06
you press fractions of these moments, what will be00:13:08
the result00:13:21
Parthenon00:13:22
Athens Greece00:13:24
people asked themselves this question two and a00:13:27
half thousand years ago,00:13:29
every July a festival was held here in00:13:32
waiting for the winner of the marathon, the spectators00:13:34
stood here and discussed various00:13:36
problems it was a festival dedicated to00:13:48
the goddess Athena the culmination of the festival was a00:13:52
parade fragments of the parade can be seen on the00:13:58
decorations taken from the temple00:14:06
these are young Athenian men boys from 1800:14:10
to 20 years old who served in the army00:14:13
they follow the parade of women riding on00:14:16
horses on the side of the road the jubilant inhabitants of00:14:21
Athens00:14:32
in the year four hundred and ninety-nine00:14:35
BC it was a major festival and00:14:39
it was an excellent opportunity for those00:14:42
who liked to show off one00:14:46
eccentric philosopher also took00:14:48
part in this festival,00:14:54
perhaps somewhere on the mountain he preached00:14:57
his strange principles00:15:11
[applause ]00:15:14
he spoke about the nature of motion his name was00:15:19
Zeno of Eletics00:15:23
Charles Safe professor of brides at the00:15:25
university Zeno was a philosopher00:15:28
who displeased all the philosophers of00:15:30
that time because he argued about00:15:33
things that seemed funny one of00:15:36
his arguments was that motion is00:15:38
impossible Zeno’s argumentation began with00:15:45
hardening since the universe00:15:49
there are no limits, Dalem reinforced his00:15:54
arguments, imagine a running competition00:15:58
between a very fast warrior with meat and a00:16:01
very slow turtle, the turtle is00:16:06
ahead of Achilles and they start running00:16:10
[applause]00:16:22
[music]00:16:26
in the end Achilles will reach the point where the00:16:31
turtle was in you, Achilles is trying00:16:39
overtake the tortoise00:16:43
but the tortoise continues to move forward00:16:49
Achilles moves forward and the tortoise too00:16:54
[music]00:16:57
so Achilles will never overtake the00:17:01
tortoise00:17:06
this does not make any sense it is strange00:17:09
but the reasoning is logical00:17:19
then Zeno's theory becomes even more00:17:21
absurd he states that no00:17:29
matter how fast a person runs he will00:17:31
never reach the finish line00:17:42
to reach the finish line the runner must00:17:45
reach the halfway mark and to00:17:49
do this he must reach half of the00:17:54
halfway if he continues he must00:17:59
reach half of any shortest00:18:01
distance00:18:11
the movement becomes impossible00:18:15
endlessly splitting up the moments we reach00:18:19
infinity the Greeks are scratching their heads00:18:26
because that in front of them there were these00:18:28
infinite parts, they could not put00:18:31
them together to go out and understand whether00:18:33
it really meant something,00:18:35
having touched infinity, they00:18:37
gave up their hands, saying it was pointless,00:18:44
one day the rain will end, like the marathon,00:18:50
one day it will end even our life00:18:59
seems useless to discuss00:19:01
infinity in reality when the end00:19:04
seems inevitable00:19:14
[music]00:19:18
Galileo was on the verge of death but survived00:19:22
instead of life imprisonment he was00:19:25
sentenced to house arrest00:19:32
calculate Florence Italy00:19:37
Galileo's last refuge was a small00:19:39
village on the outskirts of Florence00:19:49
Galileo moved to this house a year later00:19:52
after the religious trial he00:19:57
petitioned the church to be allowed00:19:59
to return to his hometown, but he was also00:20:01
refused00:20:12
[music]00:20:14
the house was preserved in the same form00:20:17
as during Galileo’s life00:20:19
[music]00:20:21
this is a modest dwelling, there is only a bed and00:20:24
a few pieces of furniture00:20:26
[music]00:20:34
but the gallery room while he could still00:20:39
see he probably looked through this00:20:41
window to the monastery where his00:20:44
daughter00:20:47
Alberta Righi once lived, not a professor at the University of Florence,00:20:50
returning from Rome, Galileo00:20:54
moved into this house, these were difficult00:20:56
times for him, he was depressed,00:20:58
his daughter, who supported him00:21:00
during the trial, suddenly died then he00:21:02
had the most severe depression he was the00:21:10
most respected scientist in Italy but he was00:21:15
brought to his knees and even worse forced to00:21:17
abandon his beliefs00:21:20
and now he is already 70 old decrepit00:21:28
he bent over the table and begins to00:21:30
write00:21:37
now he needs friends00:21:39
to argue about the rightness or00:21:42
wrongness of his logic00:21:47
[music ]00:21:57
one of them is simply siru and we suspect00:22:01
that he is a fool 2 warmed by a00:22:05
good friend who has already died00:22:08
[music]00:22:15
these characters appeared in his previous00:22:19
book00:22:20
let's listen to their conversation they00:22:30
talk about a strange wheel that00:22:32
Dansto Till was thinking about; inside the big00:22:36
wheel there is a smaller one It’s immediately00:22:40
clear that the smaller wheel has a00:22:42
smaller circumference than the larger one,00:22:50
but this is not visible if the wheels rotate00:22:54
[music]00:22:59
less and the wheel draws exactly the same00:23:02
line to you larger.00:23:05
How is this possible if these wheels have00:23:08
different circumferences00:23:10
[music]00:23:17
this is truly an amazing sight00:23:25
all wheels in the world have the same circumference00:23:35
Galileo tries to explain this00:23:38
apparent paradox00:23:39
using a hexagon when the large00:23:45
hexagon rotates00:23:47
the smaller hexagon jumps forward 1200:24:01
sides twenty-four sides00:24:05
the more sides the more jumps and the00:24:08
shorter they are00:24:09
[music]00:24:13
then the conchita line is formed00:24:17
perfect and always curious00:24:22
simply forces asks the following question,00:24:26
what about a00:24:27
lonely point answering his question00:24:35
[music]00:24:42
lines formed by a lonely point are the same00:24:45
as or unformed by a circle points and00:24:55
lines are the same conversation and00:25:00
mathematical proofs of two new00:25:02
sciences these dialogues were published in the00:25:05
book00:25:12
hearing that the larger we have00:25:15
she circle form the same line00:25:21
and the straight lines are the same00:25:24
simply seo asks the following question00:25:28
[music]00:25:35
how can I be inseparable. become a00:25:38
divisible line00:25:40
[music]00:25:47
as indivisible as I can be.00:25:50
become a divisible line the length of a line can be00:25:54
determined therefore they are limited00:25:56
it is an infinite sequence of points00:25:59
how infinite points can become a00:26:01
finite line00:26:05
then it is.00:26:10
let's turn it into a line using a00:26:12
finite amount.00:26:15
first, let's take an even number of points,00:26:19
more precisely 4, this line can be divided in00:26:23
half,00:26:28
crush the hole on q&a, what if we create a00:26:31
line with an odd number of points, the00:26:36
points cannot be divided,00:26:38
therefore, the line cannot00:26:39
be divided in half,00:26:43
cheers on the channel, in other words, the line00:26:47
must be formed from an infinite00:26:49
number of points hanging but00:26:56
[music] a00:26:58
long line has an infinite00:27:01
number of points a short line also00:27:06
has an infinite number of points what is the00:27:09
greater infinity00:27:11
[music]00:27:15
Galileo shows why it is possible00:27:18
there are an infinite number of integers00:27:21
that form a longer line00:27:24
[music]00:27:27
I will00:27:28
[music]00:27:30
now we exclude only the even ones numbers to00:27:34
create a shorter line00:27:36
[music]00:27:40
each number is interconnected with the other it00:27:46
seems that there should be more00:27:48
integers but not in this case00:27:51
[music]00:27:57
and00:27:59
whether it is infinitely large or00:28:01
infinitesimal00:28:03
[music]00:28:06
infinity is indeed a very00:28:09
strange number in the world of infinity one00:28:12
cannot argue about that small number is00:28:14
large or equal00:28:16
therefore they were left said that in the world00:28:19
of infinity one cannot argue about that00:28:21
small number large or equal00:28:29
perhaps infinity is too00:28:32
infinite a concept for the00:28:34
finite human mind to understand it00:28:38
Galili was not to blame for not00:28:40
understanding the infinite rather he was simply a00:28:43
man of his time, humanity00:28:46
was able to solve this problem only 200 years00:28:48
later there was a man who loved God00:29:02
more deeply than anyone else he00:29:05
thought about himself how can I reveal the plans of00:29:07
God here on earth then he decided to00:29:12
do this with the help of what he00:29:14
succeeded in he looked into that world in which00:29:21
no one has yet dared to look00:29:29
[applause]00:29:42
in search of infinities we found ourselves in the 19th00:29:46
century Gaul Germany did not see00:29:52
infinite large infinite small00:29:54
quantities00:29:56
but so they came face to face with00:30:00
infinity Handel was born here the00:30:08
famous composer of the 18th century00:30:14
located between Berlin and the Unified State Examination tenge00:30:16
we are quite far from the center of events00:30:18
the city of halle was exactly the place where00:30:21
ambitious young men and women came00:30:23
to make a name for themselves00:30:28
mathematician george cantor was one of those00:30:30
ambitious young people who00:30:33
came to this city to teach00:30:35
[music]00:30:43
martin luther university goglia00:30:52
professor karen richter and teaches00:30:54
mathematics at the same university,00:31:02
she also studies the life and works of Georg Kontor,00:31:05
who was a professor at this00:31:07
university a hundred years ago, Karen Richter,00:31:10
professor at the Martin Luther University,00:31:12
do people think that there is00:31:16
some kind of secret hidden in infinity and I am inclined00:31:19
to agree with them, I believe in the fact that the universe is00:31:24
infinite and completeness does not exist00:31:28
and we are able to fight with infinity00:31:35
[music]00:31:38
to fight with infinity even in our00:31:41
century to plunge into infinity means00:31:44
to invade the sphere of God but cantare had no00:31:47
doubt00:31:49
he thought that through infinity he00:31:52
could open and the kingdom of God he wanted00:31:56
see the face of God in this house in the center of the00:32:02
city Kanter lived00:32:04
Georg Kanter's house Kanter built this house00:32:13
for his family in00:32:15
1880 they moved here in 1886 and00:32:22
Kanter lived here for 40 years until his00:32:25
death00:32:30
he was a very kind and loving husband00:32:32
[music]00:32:35
Georg Kantor00:32:37
he married his sister's friend and00:32:40
became unlucky00:32:42
[music]00:32:47
but everything changed after his meeting with00:32:49
infinity00:32:51
[music]00:32:58
the world of numbers the00:33:04
world of infinity which is both00:33:06
infinitely great and infinitely small00:33:09
[music]00:33:11
cantare decides to calculate this world00:33:14
[music]00:33:15
he was inspired by Galileo cully ma00:33:21
clarty university case western reserve00:33:24
bale galileo said or said that two00:33:26
sets two collections of things are the same00:33:29
in size if i can make them00:33:31
correspond one to one but00:33:32
also he said there are as many even numbers00:33:36
as there are integers and kanter said that's00:33:38
right that's what he says about what I will say is00:33:40
true I agree with this00:33:43
before looking for infinity we00:33:45
need to know a little more about finite there00:33:50
are seats in an empty bus00:33:57
and people are waiting at the stop00:33:59
[music]00:34:01
we have more people or more empty00:34:06
seats [music]00:34:11
we can answer the this question, having seated00:34:13
people on the bus,00:34:15
it turned out that there was one more person than00:34:17
there were seats00:34:18
[music]00:34:27
canter counts the elements in infinite00:34:29
sets, how00:34:36
can you compare the sizes of infinite00:34:38
sets with finite sets,00:34:41
the road to infinity,00:34:44
many did not take this road because it00:34:47
seemed to have no end, but canter00:34:49
let's go00:34:53
[music]00:34:58
integers infinite sets now00:35:02
let's find a subset00:35:06
[music]00:35:08
first I for even numbers we will associate00:35:12
each integer with each even00:35:14
number of even numbers as many as integers00:35:17
[music]00:35:21
its00:35:25
but what about odd numbers of00:35:30
odd numbers as many as many as00:35:32
a whole00:35:33
[music]00:35:36
france there are infinitely many00:35:39
infinite sets and this opens up a00:35:42
completely new field for research not00:35:45
conter continues to develop the ideas of00:35:47
one-to-one correspondence00:35:49
he says that no matter how strange the00:35:52
results are claiming that two sets00:35:54
are the same in size00:35:55
if I can establish correspondence one00:35:57
to one and it worked as a result a00:35:59
beautiful theory was born00:36:01
in the distance there is a monument to this beautiful00:36:05
theory cantare decides to calculate the fractions00:36:14
by arranging / and sequentially he could00:36:17
compare them with integers this complex00:36:26
table changed the history of mathematics quotes from00:36:34
Kanter gives us a hint00:36:37
freedom the essence of mathematics00:36:42
to create sequence of fractions00:36:44
canter attempted the impossible00:36:49
[music]00:36:57
first he creates a sequence of00:37:00
fractions with numerator one it00:37:02
continues to infinity00:37:11
then he creates a sequence of00:37:13
fractions with numerator 200:37:15
it also continues to infinity00:37:18
[music] it's00:37:19
the turn of numerator 300:37:22
using this method canter's could00:37:24
create all infinite fractions00:37:27
[music]00:37:32
how he built their sequence00:37:35
the answer is given by the arrow00:37:40
[music] an00:37:43
infinite number of chaotic fractions00:37:46
are lined up sequentially00:37:48
[music]00:38:09
now we create a one-to-00:38:12
one correspondence with integers,00:38:14
absolutely every fraction has a pair00:38:18
[music] a00:38:23
set of integers and a set of fractions that are00:38:27
the same size00:38:29
[music]00:38:38
but the whole is greater than the part until now this00:38:44
was the key condition that made00:38:46
infinity unattainable00:38:48
but through one to00:38:50
one correspondence cantare was able to get rid of this00:38:53
error he brought us not only to the edge of00:38:56
the universe but because of him00:39:07
canter believed that his work would open the00:39:10
door to infinity the foundations of general00:39:14
set theory00:39:15
Georg Kant infinity through the prism00:39:25
of sets he thought that this work would make00:39:28
him a professor at the University of Berlin00:39:30
he was jubilant now it was possible to solve00:39:38
problems that until now had00:39:40
been unsolvable00:39:42
[music]00:39:45
this problem baffled Galileo the00:39:51
number of points in more the long00:39:53
shorter lines were the same because00:39:56
both sets were the same00:39:58
[music]00:40:04
on the square the same number of00:40:07
infinite points00:40:10
as on the line00:40:12
[music]00:40:19
the number of points on the sheet is the same as00:40:22
on the earth00:40:24
[music]00:40:30
in the world of infinity the part is as00:40:33
sufficient as and the whole00:40:36
[music]00:40:42
many mathematicians did not understand the concept of00:40:45
Kanter despite the fact that he was constantly00:40:50
criticized he was able to resist these00:40:54
attacks a hundred years ago everything was the same00:40:59
as today if you entered into scientific00:41:03
disputes they can become extremely heated it00:41:08
tempered the personality of the office00:41:10
he was Cantor's theory was not brought to fruition by a very powerful opponent00:41:33
[applause]00:41:37
and his dreams of being a professor at the00:41:39
University of Berlin were not destined to come true; he00:41:42
could not even find a publisher for his00:41:44
work; the00:41:53
29-year war in the office against his00:41:56
opponents ended sadly; the00:42:01
university's psychiatric hospital was00:42:03
far from00:42:06
Kanter's 40 years became mentally00:42:09
unstable,00:42:12
he was periodically admitted to a mental hospital00:42:20
when his attempts to obtain a position as a00:42:22
professor at the University of Berlin00:42:23
failed, he experienced a serial nervous00:42:26
breakdown,00:42:27
the doctor given by the hands of the director of the00:42:30
university psychiatric hospital and00:42:32
Harry, he had a comprehensive00:42:35
illness, he was sometimes happy and00:42:39
depressed and manic and lethargic00:42:45
he also heard voices and had00:42:50
hallucinations, he suffered from the fact that he knew00:42:54
that his mental illness could00:42:57
manifest itself at any moment, as well as from the00:43:00
ridicule of the academy, he heard the voice of God00:43:04
[music]00:43:07
I am not a mathematician, I am a messenger of God, a man00:43:14
possessed by infinity was again00:43:18
hospitalized00:43:19
it was an extremely difficult period and Kanter00:43:24
suffered a lot, he even wrote in a letter00:43:27
that because of his depression he could not00:43:32
concentrate on mathematics and could not00:43:37
continue his research,00:43:40
he felt that depression was interfering with his00:43:44
work, he00:43:51
crossed out and rewrote lines of his00:43:53
letter countless times,00:43:56
he was also meticulous in attitude towards both00:43:59
himself and mathematics00:44:08
but when his mind was clearer than ever he00:44:12
began to work with real00:44:14
numbers00:44:15
he worked with large sets00:44:17
including rational numbers00:44:20
irrational numbers and transcendental00:44:22
numbers he created a sequence of00:44:26
real numbers00:44:30
they were infinite00:44:32
they were impossible to count00:44:35
i can't proved that they cannot be00:44:37
counted regardless of the00:44:40
method used, even infinity has a size00:44:46
[music]00:44:54
but no one understood the office00:44:59
and only Kanter understood infinity00:45:06
[music]00:45:08
but infinity swallowed him up00:45:19
[music]00:45:33
she won another soul00:45:36
infinity is the place of intersection00:45:38
of the smallest and the largest and it00:45:41
was impossible to understand00:45:42
Kanter's bestiary in 1918 Georg Cantor00:45:50
died at the age of 7800:46:00
standing at his grave I think it is a00:46:06
great honor to be able to00:46:09
teach and conduct research at00:46:12
the same university as him I have00:46:19
wanted to ask him many times infinity00:46:23
we would be very interesting dialogue00:46:31
he was a mortal man who00:46:35
showed us the boundless world of00:46:36
infinity now and we saw00:46:42
infinity00:46:50
[music]Description:
#докпланета#документальныйфильм#числа#бесконечность#лестницаиакова Числа - Часть 2. Лестница Иакова Создатели документального фильма «Числа» сосредоточились на пяти цифрах, которые привели к новым открытиям в области математики, а также продвинули вперед цивилизацию. Числа «π», «∞», «x», «0», «i» были изобретены благодаря усилиям ученых в их погоне за знанием и представляют собой блестящие достижение интеллекта. Этот документальный фильм иллюстрирует красоту математики и ее глубинный смысл. Смотрите серию по ссылке: https://www.youtube.com/watch?v=eGEUiqXwISs Подписывайтесь на наш канал : https://www.youtube.com/channel/UC570zlUD71m5zrqbbfp11mA/
Preparing download options
* — If the video is playing in a new tab, go to it, then right-click on the video and select "Save video as..."
** — Link intended for online playback in specialized players
Questions about downloading video
How can I download "Числа - Часть 2. Бесконечность. Лестница Иакова - Документальный фильм" video?
http://unidownloader.com/ website is the best way to download a video or a separate audio track if you want to do without installing programs and extensions.
The UDL Helper extension is a convenient button that is seamlessly integrated into YouTube, Instagram and OK.ru sites for fast content download.
UDL Client program (for Windows) is the most powerful solution that supports more than 900 websites, social networks and video hosting sites, as well as any video quality that is available in the source.
UDL Lite is a really convenient way to access a website from your mobile device. With its help, you can easily download videos directly to your smartphone.
Which format of "Числа - Часть 2. Бесконечность. Лестница Иакова - Документальный фильм" video should I choose?
The best quality formats are FullHD (1080p), 2K (1440p), 4K (2160p) and 8K (4320p). The higher the resolution of your screen, the higher the video quality should be. However, there are other factors to consider: download speed, amount of free space, and device performance during playback.
Why does my computer freeze when loading a "Числа - Часть 2. Бесконечность. Лестница Иакова - Документальный фильм" video?
The browser/computer should not freeze completely! If this happens, please report it with a link to the video. Sometimes videos cannot be downloaded directly in a suitable format, so we have added the ability to convert the file to the desired format. In some cases, this process may actively use computer resources.
How can I download "Числа - Часть 2. Бесконечность. Лестница Иакова - Документальный фильм" video to my phone?
You can download a video to your smartphone using the website or the PWA application UDL Lite. It is also possible to send a download link via QR code using the UDL Helper extension.
How can I download an audio track (music) to MP3 "Числа - Часть 2. Бесконечность. Лестница Иакова - Документальный фильм"?
The most convenient way is to use the UDL Client program, which supports converting video to MP3 format. In some cases, MP3 can also be downloaded through the UDL Helper extension.
How can I save a frame from a video "Числа - Часть 2. Бесконечность. Лестница Иакова - Документальный фильм"?
This feature is available in the UDL Helper extension. Make sure that "Show the video snapshot button" is checked in the settings. A camera icon should appear in the lower right corner of the player to the left of the "Settings" icon. When you click on it, the current frame from the video will be saved to your computer in JPEG format.
What's the price of all this stuff?
It costs nothing. Our services are absolutely free for all users. There are no PRO subscriptions, no restrictions on the number or maximum length of downloaded videos.